Some local properties defining To-groups and related classes of groups

We call G a HallX -group if there exists a normal nilpotent subgroup N of G for which G/N0 is an X-group. We call G a T0-group provided G/Φ(G) is a T -group, that is, one in which normality is a transitive relation. We present several new local classes of groups which locally define HallX -groups an...

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Bibliographic Details
Authors: Ballester-Bolinches, Adolfo|||0000-0002-2051-9075, Beidleman, James C., Esteban-Romero, Ramon|||0000-0002-2321-8139, Ragland, Matthew F.
Format: article
Publication Date:2016
Country:España
Institution:Universitat Autònoma de Barcelona
Repository:Dipòsit Digital de Documents de la UAB
Language:English
OAI Identifier:oai:ddd.uab.cat:144969
Online Access:https://ddd.uab.cat/record/144969
https://dx.doi.org/urn:doi:10.5565/PUBLMAT_60116_10
Access Level:Open access
Keyword:Subnormal subgroup
T -group
Pst -group
Finite solvable group
Description
Summary:We call G a HallX -group if there exists a normal nilpotent subgroup N of G for which G/N0 is an X-group. We call G a T0-group provided G/Φ(G) is a T -group, that is, one in which normality is a transitive relation. We present several new local classes of groups which locally define HallX -groups and T0-groups where X ∈ {T , PT , PST }; the classes PT and PST denote, respectively, the classes of groups in which permutability and S-permutability are transitive relations. 2010 Mathematics Subject Classification: Primary: 20D10, 20D20, 20D35.